Question: Simplify; express your answer in exponential form. Assume $y\neq 0, z\neq 0$. $\dfrac{{(y)^{5}}}{{(y^{-5}z^{3})^{-2}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${y}$ to the exponent ${5}$ . Now ${1 \times 5 = 5}$ , so ${(y)^{5} = y^{5}}$ In the denominator, we can use the distributive property of exponents. ${(y^{-5}z^{3})^{-2} = (y^{-5})^{-2}(z^{3})^{-2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(y)^{5}}}{{(y^{-5}z^{3})^{-2}}} = \dfrac{{y^{5}}}{{y^{10}z^{-6}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{5}}}{{y^{10}z^{-6}}} = \dfrac{{y^{5}}}{{y^{10}}} \cdot \dfrac{{1}}{{z^{-6}}} = y^{{5} - {10}} \cdot z^{- {(-6)}} = y^{-5}z^{6}$.